arXiv research

PIML enhances machine learning for subsurface energy systems.

Subsurface applications including geothermal, geological carbon sequestration, oil and gas, etc., typically involve maximizing either the extraction of energy or the storage of fluids. Characterizing the subsurface is extremely complex due to heterogeneity and anisotropy. Due to this complexity, there are uncertainties…

Let $S_{g}$ denote the genus $g$ closed orientable surface. For $k\in \mathbb{N}$, a $k$-system is a collection of pairwise non-homotopic simple closed curves such that no two intersect more than $k$ times. Juvan-Malnič-Mohar \cite{Ju-Mal-Mo} showed that there exists a $k$-system on $S_{g}$ whose size is on the order o…

New graphs show hierarchical hyperbolic properties, extending previous work.

Random subsurfaces of hyperbolic surfaces equidistribute to ribbon graphs.

The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded if and only if the almost fiber part is aspiral, and in this ca…

The contraction of the image of the Johnson homomorphism is called the Chillingworth class. In this paper, we derive a combinatorial description of the Chillingworth class for Putman's subsurface Torelli groups. We also prove the naturality and uniqueness properties of the map whose image is the dual of the Chillingwor…

Study on compact and finite-type support in mapping class group homology.

Efficiently quantifies uncertainty in subsurface flow using neural networks guided by theory.

SAGE generates subsurface velocity models from sparse well logs and seismic images.

Proves Congruence Subgroup Property for two types of groups.

Study arcs on surfaces, focusing on topological aspects and group actions.

Combines deep generative models with ensemble methods for subsurface property estimation.

This paper is a study of the subgroups of the mapping class groups of Riemann surfaces, called "geometric" subgroups, corresponding to the inclusion of subsurfaces. Our analysis includes surfaces with boundary and with punctures. The centres of all the mapping class groups are calculated. We determine the kernel of inc…

Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly disconnected). We characterise the subsurfaces which lead to virtually abelian ge…

We compare the flat geometry associated to a quadratic differential with the hyperbolic geometry associated to the underlying Riemann surface. We show that if a curve is contained in a thick subsurface, then its hyperbolic length is comparable to its flat length times the flat size of the subsurface.

The study finds abundant normal generators for mapping class groups.

New projection complex shows some surface homeomorphisms have positive commutator length.

This paper has two main goals. First, we give a complete, explicit, and computable solution to the problem of when two simple closed curves on a surface are equivalent under the Johnson kernel. Second, we show that the Johnson filtration and the Johnson homomorphism can be defined intrinsically on subsurfaces and prove…

We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol's veering triangulation. The main theme is that large-distance subsurfaces in fibers are associated to large simplicial regions in the veering triangulation, and this correspondence holds uniformly for all…

Formula for projecting geodesics in hyperbolic 3-manifolds, relating lengths to subsurface projections.

Study classifies mapping class groups with hyperbolic actions on infinite-type surfaces.

Traditional centralized energy systems have the disadvantages of difficult management and insufficient incentives. Blockchain is an emerging technology, which can be utilized in energy systems to enhance their management and control. Integrating token economy and blockchain technology, token economic systems in energy …

Graphs of multicurves are hyperbolic, relatively hyperbolic, or thick.

The paper introduces a new differential-geometric system which originates from the theory of $m$-Hessian operators. The core of this system is a new notion of invariant differentiation on multidimensional surfaces. This novelty gives rise to the following absolute geometric invariants: invariant derivatives of the surf…

SURGIN uses generative models to infer subsurface flow data efficiently.

We show that the subsurface projection of a train track splitting sequence is an unparameterized quasi-geodesic in the curve complex of the subsurface. For the proof we introduce induced tracks, efficient position, and wide curves. This result is an important step in the proof that the disk complex is Gromov hyperbolic…

Proves conjecture about surface cover homology.

Uniform bound on geodesic images for surfaces using bicorn curves.

The article studies Hamiltonian flows on surface group representations induced by invariant multi-functions.

Proves left-orderability of mapping class groups of infinite-type surfaces.

Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomia…

By Torelli topology the author understands aspects of the topology of surfaces (potentially) relevant to the study of Torelli groups. The extension problem in Torelli topology is the problem of determining when a diffeomorphism of compact connected subsurface of a closed surface can be extended to a diffeomorphism of t…

Study quantizes energy for a specific fourth-order system in 4D.

Machine learning and deep learning infer surface/groundwater exchange from temperature data.

We give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel of the Johnson homomorphism on the Torelli subgroup of the mapping class group is generated by separating twists. In fact, we prove a more general result that also applies to "subsurface Torelli groups". Using this, we extend Joh…

Tackles dynamic subsurface flow via GAN with physical theory constraints.

New method assesses energy storage value beyond cost reduction.

In this paper, by putting a separating incompressible surface in a 3-manifold into Morse position relative to the height function associated to a strongly irreducible Heegaard splitting, we show that an incompressible subsurface of the Heegaard splitting can be found, by decomposing the 3-manifold along the separating …

Paper models uncertainty in electricity and gas markets to assess its impact.

Develops active intervals for geodesics in Teichmüller space.

Growth rates of geodesics on modular orbifolds are studied.

The curve graphs are not locally finite. In this paper, we show that the curve graphs satisfy a property which is equivalent to graphs being uniformly locally finite via Masur--Minsky's subsurface projections. As a direct application of this study, we show that there exist computable bounds for Bowditch's slices on tig…

New method reduces DSI complexity using RAE and LSTM for better posterior predictions.

Deep learning methods improve subsurface flow modeling efficiency.

Physics-informed learning framework for pH systems and EB-PBC control.

On each nonorientable surface of odd genus $g \geq 5$, we give a mapping class whose dilatation on an invariant subsurface is the golden ratio.

Johnson kernel generated by specific Dehn twists on surfaces.